SOLUTION: Write an equation that can be used to solve the problem. Then answer the question asked. The sum of the reciprocals of two consecutive even integers is 5/12. Find the 2 integers.

Question 724816: Write an equation that can be used to solve the problem. Then answer the question asked. The sum of the reciprocals of two consecutive even integers is 5/12. Find the 2 integers.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let the integers be x & x+2

multiply the equation by 12x(x+2)
12(x+2) +12x=5x(x+2)

12x+24+12x=5x^2+10x
rearrange
5x^2-14x-24=0
5x^2-20x+6x-24=0
5x(x-4)+6(x-4)=0
(x-4)(5x+6)=0
x=4 OR -6/5
ignore fraction
the numbers are 4 & 6

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